Discrete-Time Fourier Transform (DTFT) 2.10 2001/06/18 2005/03/23 15:40:21 US/Central Richard G. Baraniuk richb@rice.edu Justin Romberg jrom@rice.edu Melissa Selik mselik@alumni.rice.edu Richard G. Baraniuk richb@rice.edu Ricardo Anthony Radaelli-Sanchez ricky@alumni.rice.edu Mariyah Poonawala mariyah@rice.edu Prashant Singh prash@ece.rice.edu continuous frequency discrete time DTFT fourier transform Details the discrete-time fourier transform. Discrete-Time Fourier Transform X ω n x n ω n Inverse Discrete-Time Fourier Transform x n 1 2 ω 0 2 X ω ω n

Relevant Spaces The Discrete-Time Fourier Transform maps infinite-length, discrete-time signals in l 2 to finite-length (or 2 -periodic), continuous-frequency signals in L 2 .

Mapping l 2 in the time domain to L 2 0 2 in the frequency domain.